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Biological motivation The probabilistic model(s) Parametric estimation Adaptive estimation
Hawkes process as models for some genomic data
P. Reynaud-Bouret
CNRS - LJAD University of Nice
January 27th, Institut Curie
1/32Biological motivation The probabilistic model(s) Parametric estimation Adaptive estimation
Contents
1 Biological motivation
2/32Biological motivation The probabilistic model(s) Parametric estimation Adaptive estimation
Contents
1 Biological motivation
2 The probabilistic model(s)
2/32Biological motivation The probabilistic model(s) Parametric estimation Adaptive estimation
Contents
1 Biological motivation
2 The probabilistic model(s)
3 Parametric estimation
2/32Biological motivation The probabilistic model(s) Parametric estimation Adaptive estimation
Contents
1 Biological motivation
2 The probabilistic model(s)
3 Parametric estimation
4 Adaptive estimation
2/32Biological motivation The probabilistic model(s) Parametric estimation Adaptive estimation
Several examples
There are several ”events” of different types on the DNA that may
”work” together in synergy.
3/32Biological motivation The probabilistic model(s) Parametric estimation Adaptive estimation
Several examples
There are several ”events” of different types on the DNA that may
”work” together in synergy.
Motifs
= words in the DNA-alphabet{actg}.
3/32Biological motivation The probabilistic model(s) Parametric estimation Adaptive estimation
Several examples
There are several ”events” of different types on the DNA that may
”work” together in synergy.
Motifs
= words in the DNA-alphabet{actg}.
How can statistician suggest functional motifs based on the
statistical properties of their occurrences ?
Unexpected frequency→ Markov models (see for a review
Reinert, Schbath, Waterman (2000))
3/32Biological motivation The probabilistic model(s) Parametric estimation Adaptive estimation
Several examples
There are several ”events” of different types on the DNA that may
”work” together in synergy.
Motifs
= words in the DNA-alphabet{actg}.
How can statistician suggest functional motifs based on the
statistical properties of their occurrences ?
Unexpected frequency→ Markov models (see for a review
Reinert, Schbath, Waterman (2000))
Poor or rich regions→ scan statistics (see, for instance, Robin
Daudin (1999) or Stefanov (2003))
3/32Biological motivation The probabilistic model(s) Parametric estimation Adaptive estimation
Several examples
There are several ”events” of different types on the DNA that may
”work” together in synergy.
Motifs
= words in the DNA-alphabet{actg}.
How can statistician suggest functional motifs based on the
statistical properties of their occurrences ?
Unexpected frequency→ Markov models (see for a review
Reinert, Schbath, Waterman (2000))
Poor or rich regions→ scan statistics (see, for instance, Robin
Daudin (1999) or Stefanov (2003))
If two motifs are part of a common biological process, the
space between their occurrences (not necessarily consecutive)
should be somehow fixed→ favored or avoided distances
(Gusto, Schbath (2005))
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